Is John Churchill related to Winston Churchill?

The "Cavalier Colonel" Winston Churchill (1620-1688) was the father of the general John Churchill, 1st Duke of Malborough (1650-1722). The 1st Duke's third daughter, Anne Churchill Spencer (1683-1716), was the ancestor of both the modern Winston Churchill and Diana Spencer, Princess of Wales, through her sons Charles and John.
The Churchill surname was resurrected by George Spencer, the 5th Duke of Malborough (1766-1840), and adopted by his son George Spencer-Churchill (6th Duke, 1793-1857) and his grandson John Winston Spencer-Churchill (7th Duke, 1822-1883), who was the grandfather of both prime minister Winston Churchill (1874-1965) and his younger brother Major John "Jack" Spencer-Churchill (1880-1947).
(This makes the former prime minister the great-great-great-great-great-great-grandson of his famous namesake colonel.)